Question: The manager of a minor league baseball

> Assume that X is a hypergeometric random variable with N = 15, S = 4, and n = 3. Calculate the following probabilities. a. P (X = 1) b. P (X = 2) c. P (X ≥ 2)

> An extended warranty is a prolonged warranty offered to consumers by the warranty administrator, the retailer, or the manufacturer. A report in The New York Times (November 23, 2009) suggests that 20.4% of laptops fail over three years. Roberto Dâ&

> A hospital administrator worries about the possible loss of electric power as a result of a power blackout. The hospital, of course, has a standby generator, but it, too, is subject to failure, having a mean time between failures of 500 hours. It is reas

> In the fiscal year that ended September 30, 2008, there were 24,584 age-discrimination claims filed with the Equal Employment Opportunity Commission, an increase of 29% from the previous year (The Wall Street Journal, March 7−8, 2009). Assume there were

> Due to the advent of tablets, American adults are watching significantly less television than they did in previous decades. In 2016, Nielsen reported that American adults are watching an average of five hours and four minutes, or 304 minutes, of televisi

> According to a government report, the aging of the U.S. population is translating into many more visits to doctors’ offices and hospitals (USA Today, August 7, 2008). It is estimated that an average person makes four visits a year to doctors’ offices and

> On average, 400 people are struck by lightning in the United States each year (The Boston Globe, July 21, 2008). a. What is the probability that at most 425 people are struck by lightning in a year? b. What is the probability that at least 375 people are

> Let Y have the lognormal distribution with mean 82.8 and variance 156.25. Compute the following probabilities. a. P (Y > 100) b. P (80 < Y < 100)

> Let Y = eX, where X is normally distributed. Compute the mean and the variance of X given the following information. a. μY = 14, σ2Y = 22 b. μY = 20, σ2Y = 22 c. μY = 20, σ2Y = 120

> Let Y = eX where X is normally distributed with μ = 1.8 and σ = 0.80. Compute the following values. a. P(Y ≤ 7.5) b. P(8 < Y < 9) c. The 90th percentile of Y

> Compute the mean and the variance of a lognormal variable Y = eX where X is normally distributed with the following mean and variance: a. μ = 3, σ2 = 2 b. μ = 5, σ2 = 2 c. μ = 5, σ2 = 3

> On average, there are 12 potholes per mile on a particular stretch of the state highway. Suppose the potholes are distributed evenly on the highway. a. Find the probability of finding fewer than two potholes in a quarter-mile stretch of the highway. b. F

> An economist reports that 560 out of a sample of 1,200 middle-income American households actively participate in the stock market. a. Construct the 90% confidence interval for the proportion of middle-income Americans who actively participate in the stoc

> Which of the following scenarios are likely to represent Poisson random variables? a. The number of violent crimes in New York over a six-week period. b. The number of customers of a bank manager who will default. c. The number of scratches on a 2-by-1-f

> Which of the following probabilities are likely to be found using a Poisson distribution? a. The probability that there will be six leaks in a specified stretch of a pipeline. b. The probability that at least 10 students in a class of 40 will land a job

> Assume that X is a Poisson random variable with μ = 15. Calculate the following probabilities. a. P (X ≤ 10) b. P (X = 13) c. P (X > 15) d. P (12 ≤ X ≤ 18)

> The mileage (in 1,000s of miles) that car owners get with a certain kind of radial tire is a random variable Y having a lognormal distribution such that Y = eX, where X is normally distributed. Let the mean and the standard deviation of the life of a rad

> On average, a certain kind of kitchen appliance requires repairs once every four years. Assume that the times between repairs are exponentially distributed. a. What is the probability that the appliance will work no more than three years without requirin

> The relief time provided by a standard dose of a popular children’s allergy medicine averages six hours with a standard deviation of two hours. a. Determine the percentage of children who experience relief for less than four hours if the relief time foll

> In a local law office, jobs to a printer are sent at a rate of 8 jobs per hour. Suppose that the number of jobs sent to a printer follows the Poisson distribution. a. What is the expected time between successive jobs? b. What is the probability that the

> Suppose that the average IQ score is normally distributed with a mean of 100 and a standard deviation of 16. a. What is the probability a randomly selected person will have an IQ score of less than 80? b. What is the probability that a randomly selected

> The length of components produced by a company is normally distributed with a mean of 6 cm and a standard deviation of 0.02 cm. Calculate the first, second, and third quartiles of the component length.

> The average household income in a community is known to be $80,000. Also, 20% of the households have an income below $60,000 and another 20% have an income above $90,000. Is it reasonable to use the normal distribution to model the household income in th

> In a CNNMoney.com poll conducted on July 13, 2010, a sample of 5,324 Americans were asked about what matters most to them in a place to live. Thirty-seven percent of the respondents felt job opportunities matter most. a. Construct the 90% confidence inte

> On St. Patrick’s Day, men spend an average of $43.87 while women spend an average of $29.54 (USA TODAY, March 17, 2009). Assume the standard deviations of spending for men and women are $3 and $11, respectively, and that both distributions are normally d

> The revised guidelines from the National High Blood Pressure Education Program define normal blood pressure as readings below 120/80 millimeters of mercury (The New York Times, May 14, 2003). Prehypertension is suspected when the top number (systolic) is

> A worker at a landscape design center uses a machine to fill bags with potting soil. Assume that the quantity put in each bag follows the continuous uniform distribution with low and high filling weights of 10 pounds and 12 pounds, respectively. a. Calcu

> It is well documented that a typical washing machine can last anywhere between 5 to 12 years. Let the life of a washing machine be represented by a lognormal variable, Y = eX, where X is normally distributed. In addition, let the mean and standard deviat

> Motorists arrive at a Gulf station at the rate of two per minute during morning hours. Assume that the arrival of motorists at the station follows a Poisson distribution. a. What is the probability that the next car’s arrival is in less than one minute?

> The Bahamas is a tropical paradise made up of 700 islands sprinkled over 100,000 square miles of the Atlantic Ocean. According to the figures released by the government of the Bahamas, the mean household income in the Bahamas is $39,626 and the median in

> Many U.S. households still do not have Internet access. Suppose 20 out of 80 households in a small southern town do not have Internet access. A company that provides high-speed Internet has recently entered the market. As part of the marketing campaign,

> Assume that X is a Poisson random variable with μ = 15. Calculate the following probabilities. a. P (X ≤ 10) b. P (X = 13) c. P (X > 15) d. P (12 ≤ X ≤ 18)

> Assume a Poisson random variable has a mean of four arrivals over a 10-minute interval. a. What is the mean of the random variable, defined by the time between arrivals? b. Find the probability that the next arrival would be within the mean time. c. Find

> Assume a Poisson random variable has a mean of 6 successes over a 120-minute period. a. Find the mean of the random variable, defined by the time between successes. b. What is the rate parameter of the appropriate exponential distribution? c. Find the pr

> The Gallup-Healthways Well-Being Index (www.well-beingindex.com) provides an assessment measure of health and well-being of U.S. residents. By collecting periodic data on life evaluation, physical health, emotional health, healthy behavior, work environm

> A certain brand of refrigerators has a length of life that is normally distributed with a mean and a standard deviation of 15 years and 2 years, respectively. a. What is the probability a refrigerator will last less than 6.5 years? b. What is the probabi

> A new car battery is sold with a two-year warranty whereby the owner gets the battery replaced free of cost if it breaks down during the warranty period. Suppose an auto store makes a net profit of $20 on batteries that stay trouble-free during the warra

> At the University of Notre Dame Mendoza College of Business, 40% of the students seeking a master’s degree specialize in finance (Kiplinger’s Personal Finance, March 2009). Twenty master’s degree students are randomly selected. a. What is the probability

> According to a report by the PEW Research Center, 85% of adults under 30 feel optimistic about the economy, but the optimism is shared by only 45% of those who are over 50 (Newsweek, September 13, 2010). A research analyst would like to construct 95% con

> An employee of the Bureau of Transportation Statistics has been given the task of estimating the proportion of on-time arrivals of a budget airline. A prior study had estimated this on-time arrival rate as 78.5%. What is the minimum number of arrivals th

> An economist would like to estimate the 95% confidence interval for the average real estate taxes collected by a small town in California. In a prior analysis, the standard deviation of real estate taxes was reported as $1,580. What is the minimum sample

> Suppose 40% of recent college graduates plan on pursuing a graduate degree. Fifteen recent college graduates are randomly selected. a. What is the probability that no more than four of the college graduates plan to pursue a graduate degree? b. What is th

> Research suggests that Americans make an average of 10 phone calls per day (CNN, August 26, 2010). Let the number of calls be normally distributed with a standard deviation of 3 calls. a. What is the probability that an average American makes between 4 a

> Linda Barnes has learned from prior studies that one out of five applicants gets admitted to top MBA programs in the country. She wishes to construct her own 90% confidence interval for the acceptance rate in top MBA programs. How large a sample should s

> A Monster.com poll of 3,057 individuals asked: “What’s the longest vacation you plan to take this summer?” The following relative frequency distribution summarizes the results. Response ……………………………………………………………………… Relative Frequency A few days ………………………

> A poll of 1,079 adults found that 51% of Americans support Arizona’s stringent new immigration enforcement law, even though it may lead to racial profiling (The New York Times/CBS News, April 28–May 2, 2010). Use the sample information to compute the 95%

> According to a survey of 1,235 businesses by IDC, a market-research concern in Framingham, Massachusetts, 12.1% of sole proprietors are engaging in e-commerce (The Wall Street Journal, July 26, 2007). a. With 95% confidence, what is the margin of error w

> Real estate investment in college towns continues to promise good returns (The Wall Street Journal, September 24, 2010). Marcela Treisman works for an investment firm in Michigan. Her assignment is to analyze the rental market in Ann Arbor, which is home

> A construction company in Naples, Florida, is struggling to sell condominiums. In order to attract buyers, the company has made numerous price reductions and better financing offers. Although condominiums were once listed for $300,000, the company believ

> Residents of Hawaii have the longest life expectancies, averaging 81.48 years (www.worldlifeexpectancy.com, data retrieved June 4, 2012). A sociologist collects data on the age at death for 50 recently deceased Michigan residents. A portion of the data i

> A realtor wants to estimate the mean price of houses in Mission Viejo, California. She collects a sample of 36 recent house sales (in $1,000s), a portion of which is shown in the accompanying table. Assume that the population standard deviation is 100 (i

> The following table shows the annual returns (in percent) for the Vanguard Energy Fund. Year …………………………………………………………………………………………… Return 2010 …………………………………………………………………………………………………. 13 2011 …………………………………………………………………………………………………. −2 2012 ………………………………………………

> A study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving (The Wall Street Journal, May 5, 2010). Suppose this study was based on a random sample of 50 teen drivers. a. Construct the 99% confidence interval for the

> The SAT is the most widely used test in the undergraduate admissions process. Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Ha

> Loans that are 60 days or more past due are considered seriously delinquent. The Mortgage Bankers Association reported that the rate of seriously delinquent loans has an average of 9.1% (The Wall Street Journal, August 26, 2010). Let the rate of seriousl

> In a sample of 30 observations, the number of successes equals 18. a. Construct the 88% confidence interval for the population proportion of successes. b. Construct the 98% confidence interval for the population proportion of successes. c. What happens t

> Students who graduated from college in 2010 owed an average of $25,250 in student loans (The New York Times, November 2, 2011). An economist wants to determine if average debt has changed. She takes a sample of 40 recent graduates and finds that their av

> Recently, six single-family homes in San Luis Obispo County in California sold at the following prices (in $1,000s): 549, 449, 705, 529, 639, and 609. a. Construct the 95% confidence interval for the mean sale price in San Luis Obispo County. b. What ass

> According to data from the Organization for Economic Cooperation and Development, the average U.S. worker takes 16 days of vacation each year (The Wall Street Journal, June 20, 2007). Assume that these data were based on a sample of 225 workers and that

> A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 40, 30, 28, 22, 36, 16, and 50. It can be assumed that weekday customer visits follow a normal distribution. a.

> Over a 10-year sample period, the mean and the standard deviation of annual returns on a portfolio you are analyzing were 10% and 15%, respectively. You assume that returns are normally distributed. Construct the 95% confidence interval for the populatio

> A business student is interested in estimating the 99% confidence interval for the proportion of students who bring laptops to campus. He wishes a precise estimate and is willing to draw a large sample that will keep the sample proportion within five per

> Subprime lending was big business in the United States in the mid-2000s, when lenders provided mortgages to people with poor credit. However, subsequent increases in interest rates coupled with a drop in home values necessitated many borrowers to default

> On average, an American professional football game lasts about three hours, even though the ball is actually in play only 11 minutes (www.sportsgrid.com, January 14, 2014). Assume that game times are normally distributed with a standard deviation of 0.4

> Newscasters wish to estimate the proportion of registered voters who support the incumbent candidate in the mayoral election. In an earlier poll of 240 registered voters, 110 had supported the incumbent candidate. Find the sample size required to constru

> A budget airline wants to estimate what proportion of customers would consider paying $12 for in-flight wireless access. Given that the airline has no prior knowledge of the proportion, how many customers would it have to sample to ensure a margin of err

> A random sample of 100 observations results in 40 successes. a. What is the point estimate for the population proportion of successes? b. Construct 90% and 99% confidence intervals for the population proportion. c. Can we conclude at 90% confidence that

> The manager of a newly opened Target store wants to estimate the average expenditure of his customers. From a preselected sample, the standard deviation was determined to be $18. The manager would like to construct the 95% confidence interval for the mea

> The manager of a pizza chain in Albuquerque, New Mexico, wants to determine the average size of their advertised 16-inch pizzas. She takes a random sample of 25 pizzas and records their mean and standard deviation as 16.10 inches and 1.8 inches, respecti

> An analyst would like to construct 95% confidence intervals for the mean stock returns in two industries. Industry A is a high-risk industry with a known population standard deviation of 20.6%, whereas Industry B is a low-risk industry with a known popul

> An analyst from an energy research institute in California wishes to estimate the 99% confidence interval for the average price of unleaded gasoline in the state. In particular, she does not want the sample mean to deviate from the population mean by mor

> Mortgage lenders often use FICO scores to check the credit worthiness of consumers applying for real estate loans. In general, FICO scores range from 300 to 850 with higher scores representing a better credit profile. A lender in a Midwestern town would

> You wish to compute the 95% confidence interval for the population proportion. How large a sample should you draw to ensure that the sample proportion does not deviate from the population proportion by more than 0.06? No prior estimate for the population

> According to the Bureau of Labor Statistics, it takes an average of 22 weeks for someone over 55 to find a new job, compared with 16 weeks for younger workers (The Wall Street Journal, September 2, 2008). Assume that the probability distributions are nor

> Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normally distributed random variable with a mean and a standard deviation of 33.8 mpg and 3.5 mpg, respectively. a. What is the probability that a randomly selected passenger car gets

> A professional basketball team averages 80 points per game with a standard deviation of 10 points. Assume points per game follow the normal distribution. a. What is the probability that a game’s score is between 60 and 100 points? b. What is the probabil

> You need to compute the 99% confidence interval for the population mean. How large a sample should you draw to ensure that the sample mean does not deviate from the population mean by more than 1.2? (Use 6.0 as an estimate of the population standard devi

> A sample of 80 results in 30 successes. a. Calculate the point estimate for the population proportion of successes. b. Construct 90% and 99% confidence intervals for the population proportion. c. Can we conclude at 90% confidence that the population prop

> Find the required sample size for estimating the population mean in order to be 95% confident that the sample mean is within 10 units of the population mean. Assume that the population standard deviation is 40.

> At a local community college, 40% of students who enter the college as freshmen go on to graduate. Ten freshmen are randomly selected. a. What is the probability that none of them graduates from the local community college? b. What is the probability tha

> The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 16 minutes and 4 minutes, respectively. a. Find the probability that a randomly picked assembly takes between 10 and 20 minutes. b. It i

> Let X represent a binomial random variable with n = 200 and p = 0.77. Find the following probabilities. a. P (X ≤ 150) b. P (X > 160) c. P (155 ≤ X ≤ 165) d. P (X = 160)

> A survey conducted by CBS News asked 1,026 respondents: “What would you do with an unexpected tax refund?” The responses are summarized in the following table. Response ………………………………………………………………………………... Frequency Pay off debts ……………………………………………………………………

> An accounting professor is notorious for being stingy in giving out good letter grades. In a large section of 140 students in the fall semester, she gave out only 5% A’s, 23% B’s, 42% C’s, and 30% D’s and F’s. Assuming that this was a representative clas

> Let X represent a binomial random variable with n = 150 and p = 0.36. Find the following probabilities. a. P (X ≤ 50) b. P (X = 40) c. P (X > 60) d. P (X ≥ 55)

> In a recent poll of 760 homeowners in the United States, one in five homeowners reports having a home equity loan that he or she is currently paying off. Using a confidence coefficient of 0.90, derive the interval estimate for the proportion of all homeo

> In an NBC News/Wall Street Journal poll of 1,000 American adults conducted August 5–9, 2010, 44% of respondents approved of the job that Barack Obama was doing in handling the economy. a. Compute the 90% confidence interval for the proportion of American

> The average rent in a city is $1,500 per month with a standard deviation of $250. Assume rent follows the normal distribution. a. What percentage of rents are between $1,250 and $1,750? b. What percentage of rents are less than $1,250? c. What percentage

> Assume in a sample of size n = 50. a. Construct the 95% confidence interval for the population proportion. b. What happens to the margin of error if the above sample proportion is based on n = 200 instead of n = 50?

> Assume that IQ scores follow a normal distribution with a mean of 100 and a standard deviation of 16. a. What is the probability that an individual scores between 84 and 116? b. What is the probability that an individual scores less than 68? c. What is t

> A survey of 1,026 people asked: “What would you do with an unexpected tax refund?” Forty-seven percent responded that they would pay off debts (Vanity Fair, June 2010). a. At 95% confidence, what is the margin of error? b. Construct the 95% confidence in

> According to a company’s website, the top 25% of the candidates who take the entrance test will be called for an interview. You have just been called for an interview. The reported mean and standard deviation of the test scores are 68 and 8, respectively

> Assume that X is a binomial random variable with n = 5 and p = 0.35. Calculate the following probabilities. a. P (X = 0) b. P (X = 1) c. P (X ≤ 1)

> The weight of turkeys is normally distributed with a mean of 22 pounds and a standard deviation of 5 pounds. a. Find the probability that a randomly selected turkey weighs between 20 and 26 pounds. b. Find the probability that a randomly selected turkey

> Americans are increasingly skimping on their sleep (National Geographic News, February 24, 2005). A health expert believes that American adults sleep an average of 6.2 hours on weekdays, with a standard deviation of 1.2 hours. Assume that sleep time on w

> The average high school teacher annual salary is $43,000 (Payscale.com, August 20, 2010). Let teacher salary be normally distributed with a standard deviation of $18,000. a. What percentage of high school teachers make between $40,000 and $50,000? b. Wha

> A portfolio has $200,000 invested in Asset X and $300,000 in Asset Y. Consider the summary measures in the following table. a. Calculate the portfolio weights for assets X and Y. b. Calculate the expected return for the portfolio. c. Calculate the stan

> Many of today’s leading companies, including Google, Microsoft, and Facebook, are based on technologies developed within universities. Lisa Fisher is a business school professor who believes that a university’s research expenditure (Research in $ million

> You own a portfolio that has $4,400 invested in stocks and $5,600 invested in bonds. What is the expected return of the portfolio if stocks and bonds are expected to yield a return of 9% and 5%, respectively?

> A random sample of 80 observations results in 50 successes. a. Construct the 95% confidence interval for the population proportion of successes. b. Construct the 95% confidence interval for the population proportion of failures.